The diagnosis setup is shown in Fig. REF , where the IRS is operating at the mmWave band and is the system to be diagnosed.
The IRS is in uniform planar array (UPA) structure and consists of \(N = H \times W\)  reflecting elements, where \(H\)  and \(W\)  are the number of elements along vertical and horizontal directions, respectively.
Both the TX and the RX are equipped with a single antenna.The extension to multi-antenna RX will be presented in Sec. REF .
The fault-free received signal at the RX can be expressed as [1]}
\(y^{\prime } = \left(\mathbf {h}_\mathrm {RX}^\mathrm {T} \Gamma  \mathbf {h}_\mathrm {TX} + h_\mathrm {D} \right) x + w^{\prime },\) 
